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<div class="title">PolynomialSolver.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2010 Manuel Yguel &lt;manuel.yguel@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_POLYNOMIAL_SOLVER_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_POLYNOMIAL_SOLVER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> Scalar_, <span class="keywordtype">int</span> Deg_ &gt;</div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html">   31</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;{</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Deg_==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : Deg_)</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    <span class="keyword">typedef</span> Scalar_                             Scalar;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a>    RealScalar;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <span class="keyword">typedef</span> std::complex&lt;RealScalar&gt;            RootType;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keyword">typedef</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;RootType,Deg_,1&gt;</a>             <a class="codeRef" href="../classEigen_1_1Matrix.html">RootsType</a>;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keyword">typedef</span> DenseIndex Index;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> setPolynomial( <span class="keyword">const</span> OtherPolynomial&amp; poly ){</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;      m_roots.<a class="codeRef" href="../classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(poly.size()-1); }</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160; </div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a>( <span class="keyword">const</span> OtherPolynomial&amp; poly ){</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;      setPolynomial( poly() ); }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a>(){}</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#ae315ff89bf2811db0b9378fdf9bdae11">   57</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">RootsType</a>&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#ae315ff89bf2811db0b9378fdf9bdae11">roots</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_roots; }</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Stl_back_insertion_sequence&gt;</div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a8dc272fb0a2139fd2b5454d1e947a7da">   71</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a8dc272fb0a2139fd2b5454d1e947a7da">realRoots</a>( Stl_back_insertion_sequence&amp; bi_seq,</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;      <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;      bi_seq.clear();</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;      <span class="keywordflow">for</span>(Index i=0; i&lt;m_roots.size(); ++i )</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;      {</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keywordflow">if</span>( <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) &lt; absImaginaryThreshold ){</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;          bi_seq.push_back( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">real</a>() ); }</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;      }</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    }</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160; </div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> squaredNormBinaryPredicate&gt;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RootType&amp; selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate&amp; pred )<span class="keyword"> const</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> res=0;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      RealScalar norm2 = numext::abs2( m_roots[0] );</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;      <span class="keywordflow">for</span>( <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1; i&lt;m_roots.size(); ++i )</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;      {</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="keyword">const</span> RealScalar currNorm2 = numext::abs2( m_roots[i] );</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        <span class="keywordflow">if</span>( pred( currNorm2, norm2 ) ){</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;          res=i; norm2=currNorm2; }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;      }</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;      <span class="keywordflow">return</span> m_roots[res];</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    }</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a6d8e134d014023b692b0cabea57b8d99">  102</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RootType&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a6d8e134d014023b692b0cabea57b8d99">greatestRoot</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;      std::greater&lt;RealScalar&gt; greater;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;      <span class="keywordflow">return</span> selectComplexRoot_withRespectToNorm( greater );</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    }</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a7512d659658ff8b70f333768f9e4bdf6">  111</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RootType&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a7512d659658ff8b70f333768f9e4bdf6">smallestRoot</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;      std::less&lt;RealScalar&gt; less;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;      <span class="keywordflow">return</span> selectComplexRoot_withRespectToNorm( less );</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    }</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160; </div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> squaredRealPartBinaryPredicate&gt;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; selectRealRoot_withRespectToAbsRealPart(</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        squaredRealPartBinaryPredicate&amp; pred,</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;      <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;      hasArealRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> res=0;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;      RealScalar <a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a>(0);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;      <span class="keywordflow">for</span>( <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=0; i&lt;m_roots.size(); ++i )</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;      {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        <span class="keywordflow">if</span>( <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) &lt;= absImaginaryThreshold )</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        {</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;          <span class="keywordflow">if</span>( !hasArealRoot )</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;          {</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            hasArealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            res = i;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            <a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a> = m_roots[i].real() * m_roots[i].real();</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;          }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;          <span class="keywordflow">else</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;          {</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;            <span class="keyword">const</span> RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real();</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="keywordflow">if</span>( pred( currAbs2, <a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a> ) )</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;            {</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;              <a class="codeRef" href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">abs2</a> = currAbs2;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;              res = i;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;            }</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;          }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        }</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(!hasArealRoot)</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        {</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;          <span class="keywordflow">if</span>( <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) &lt; <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[res].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) ){</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            res = i;}</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        }</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;      }</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;      <span class="keywordflow">return</span> numext::real_ref(m_roots[res]);</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    }</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RealPartBinaryPredicate&gt;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; selectRealRoot_withRespectToRealPart(</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        RealPartBinaryPredicate&amp; pred,</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = NumTraits&lt;Scalar&gt;::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;      hasArealRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;      <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> res=0;</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      RealScalar val(0);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160; </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;      <span class="keywordflow">for</span>( Index i=0; i&lt;m_roots.size(); ++i )</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;      {</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        <span class="keywordflow">if</span>( <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) &lt;= absImaginaryThreshold )</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;          <span class="keywordflow">if</span>( !hasArealRoot )</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;          {</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;            hasArealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;            res = i;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;            val = m_roots[i].real();</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;          }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;          <span class="keywordflow">else</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;          {</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;            <span class="keyword">const</span> RealScalar curr = m_roots[i].real();</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;            <span class="keywordflow">if</span>( pred( curr, val ) )</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;            {</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;              val = curr;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;              res = i;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;            }</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;          }</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        }</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;          <span class="keywordflow">if</span>( <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[i].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) &lt; <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>( m_roots[res].<a class="codeRef" href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">imag</a>() ) ){</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            res = i; }</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        }</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;      }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;      <span class="keywordflow">return</span> numext::real_ref(m_roots[res]);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00214"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#ade5cd822a659dc18f4e8b674d477bec0">  214</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#ade5cd822a659dc18f4e8b674d477bec0">absGreatestRealRoot</a>(</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;      std::greater&lt;RealScalar&gt; greater;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      <span class="keywordflow">return</span> selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    }</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#ad2438282277bbb62960c3ad1f286052b">  237</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#ad2438282277bbb62960c3ad1f286052b">absSmallestRealRoot</a>(</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;      std::less&lt;RealScalar&gt; less;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;      <span class="keywordflow">return</span> selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    }</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a85d21a3516e60e6af12898b36e7a016f">  260</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a85d21a3516e60e6af12898b36e7a016f">greatestRealRoot</a>(</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;      std::greater&lt;RealScalar&gt; greater;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;      <span class="keywordflow">return</span> selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    }</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#abacd1d52145ce7bdc6f070380eac3b2d">  283</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1PolynomialSolverBase.html#abacd1d52145ce7bdc6f070380eac3b2d">smallestRealRoot</a>(</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        <span class="keywordtype">bool</span>&amp; hasArealRoot,</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        <span class="keyword">const</span> RealScalar&amp; absImaginaryThreshold = <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::dummy_precision</a>() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;      std::less&lt;RealScalar&gt; less;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;      <span class="keywordflow">return</span> selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    }</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160; </div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    RootsType               m_roots;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;};</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="preprocessor">#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE )  \</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="preprocessor">  typedef typename BASE::Scalar                 Scalar;       \</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;<span class="preprocessor">  typedef typename BASE::RealScalar             RealScalar;   \</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;<span class="preprocessor">  typedef typename BASE::RootType               RootType;     \</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="preprocessor">  typedef typename BASE::RootsType              RootsType;</span></div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160; </div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar_, <span class="keywordtype">int</span> Deg_&gt;</div>
<div class="line"><a name="l00333"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolver.html">  333</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1PolynomialSolver.html">PolynomialSolver</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a>&lt;Scalar_,Deg_&gt;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;{</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,Deg_==<a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : Deg_)</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160; </div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase&lt;Scalar_,Deg_&gt;</a>    <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PS_Base</a>;</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PS_Base</a> )</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160; </div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <span class="keyword">typedef</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Deg_,Deg_&gt;</a>                 <a class="codeRef" href="../classEigen_1_1Matrix.html">CompanionMatrixType</a>;</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    <span class="keyword">typedef</span> std::conditional_t&lt;NumTraits&lt;Scalar&gt;::IsComplex,</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;                                    <a class="codeRef" href="../classEigen_1_1ComplexEigenSolver.html">ComplexEigenSolver&lt;CompanionMatrixType&gt;</a>,</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;                                    <a class="codeRef" href="../classEigen_1_1EigenSolver.html">EigenSolver&lt;CompanionMatrixType&gt;</a> &gt; EigenSolverType;</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    <span class="keyword">typedef</span> std::conditional_t&lt;NumTraits&lt;Scalar&gt;::IsComplex, Scalar, std::complex&lt;Scalar&gt; &gt; ComplexScalar;</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160; </div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00350"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">  350</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">compute</a>( <span class="keyword">const</span> OtherPolynomial&amp; poly )</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    {</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      eigen_assert( Scalar(0) != poly[poly.size()-1] );</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      eigen_assert( poly.size() &gt; 1 );</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;      <span class="keywordflow">if</span>(poly.size() &gt;  2 )</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      {</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        internal::companion&lt;Scalar,Deg_&gt; companion( poly );</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;        companion.balance();</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        m_eigenSolver.compute( companion.denseMatrix() );</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        m_roots = m_eigenSolver.eigenvalues();</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        <span class="comment">// cleanup noise in imaginary part of real roots:</span></div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;        <span class="comment">// if the imaginary part is rather small compared to the real part</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;        <span class="comment">// and that cancelling the imaginary part yield a smaller evaluation,</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;        <span class="comment">// then it&#39;s safe to keep the real part only.</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;        RealScalar coarse_prec = RealScalar(std::pow(4,poly.size()+1))*<a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;        <span class="keywordflow">for</span>(Index i = 0; i&lt;m_roots.size(); ++i)</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;        {</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;          <span class="keywordflow">if</span>( internal::isMuchSmallerThan(numext::abs(numext::imag(m_roots[i])),</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;                                          numext::abs(numext::real(m_roots[i])),</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;                                          coarse_prec) )</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;          {</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;            ComplexScalar as_real_root = ComplexScalar(numext::real(m_roots[i]));</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;            <span class="keywordflow">if</span>(    numext::abs(<a class="code" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">poly_eval</a>(poly, as_real_root))</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;                &lt;= numext::abs(<a class="code" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">poly_eval</a>(poly, m_roots[i])))</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;            {</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;              m_roots[i] = as_real_root;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;            }</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;          }</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        }</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;      }</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(poly.size () == 2)</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;      {</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;        m_roots.<a class="codeRef" href="../classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(1);</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;        m_roots[0] = -poly[0]/poly[1];</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;      }</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    }</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160; </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolver.html">PolynomialSolver</a>( <span class="keyword">const</span> OtherPolynomial&amp; poly ){</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;      <a class="code" href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">compute</a>( poly ); }</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160; </div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="keyword">inline</span> PolynomialSolver(){}</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160; </div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    <span class="keyword">using</span>                   PS_Base::m_roots;</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    EigenSolverType         m_eigenSolver;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;};</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160; </div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160; </div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="keyword">template</span>&lt; <span class="keyword">typename</span> Scalar_ &gt;</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="keyword">class </span>PolynomialSolver&lt;Scalar_,1&gt; : <span class="keyword">public</span> PolynomialSolverBase&lt;Scalar_,1&gt;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;{</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    <span class="keyword">typedef</span> PolynomialSolverBase&lt;Scalar_,1&gt;    PS_Base;</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">compute</a>( <span class="keyword">const</span> OtherPolynomial&amp; poly )</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    {</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;      eigen_assert( poly.size() == 2 );</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;      eigen_assert( Scalar(0) != poly[1] );</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;      m_roots[0] = -poly[0]/poly[1];</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    }</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160; </div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> OtherPolynomial &gt;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    <span class="keyword">inline</span> PolynomialSolver( <span class="keyword">const</span> OtherPolynomial&amp; poly ){</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;      <a class="code" href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">compute</a>( poly ); }</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;    <span class="keyword">inline</span> PolynomialSolver(){}</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    <span class="keyword">using</span>                   PS_Base::m_roots;</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;};</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160; </div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160; </div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_POLYNOMIAL_SOLVER_H</span></div>
<div class="ttc" id="aclassEigen_1_1ComplexEigenSolver_html"><div class="ttname"><a href="../classEigen_1_1ComplexEigenSolver.html">Eigen::ComplexEigenSolver</a></div></div>
<div class="ttc" id="aclassEigen_1_1EigenSolver_html"><div class="ttname"><a href="../classEigen_1_1EigenSolver.html">Eigen::EigenSolver</a></div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="../classEigen_1_1Matrix.html">Eigen::Matrix&lt; RootType, Deg_, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a9fd0703bd7bfe89d6dc80e2ce87c312a"><div class="ttname"><a href="../classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">Eigen::PlainObjectBase::resize</a></div><div class="ttdeci">void resize(Index rows, Index cols)</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html">Eigen::PolynomialSolverBase</a></div><div class="ttdoc">Defined to be inherited by polynomial solvers: it provides convenient methods such as.</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:32</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_a6d8e134d014023b692b0cabea57b8d99"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a6d8e134d014023b692b0cabea57b8d99">Eigen::PolynomialSolverBase::greatestRoot</a></div><div class="ttdeci">const RootType &amp; greatestRoot() const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:102</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_a7512d659658ff8b70f333768f9e4bdf6"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a7512d659658ff8b70f333768f9e4bdf6">Eigen::PolynomialSolverBase::smallestRoot</a></div><div class="ttdeci">const RootType &amp; smallestRoot() const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:111</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_a85d21a3516e60e6af12898b36e7a016f"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a85d21a3516e60e6af12898b36e7a016f">Eigen::PolynomialSolverBase::greatestRealRoot</a></div><div class="ttdeci">const RealScalar &amp; greatestRealRoot(bool &amp;hasArealRoot, const RealScalar &amp;absImaginaryThreshold=NumTraits&lt; Scalar &gt;::dummy_precision()) const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:260</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_a8dc272fb0a2139fd2b5454d1e947a7da"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a8dc272fb0a2139fd2b5454d1e947a7da">Eigen::PolynomialSolverBase::realRoots</a></div><div class="ttdeci">void realRoots(Stl_back_insertion_sequence &amp;bi_seq, const RealScalar &amp;absImaginaryThreshold=NumTraits&lt; Scalar &gt;::dummy_precision()) const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_abacd1d52145ce7bdc6f070380eac3b2d"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#abacd1d52145ce7bdc6f070380eac3b2d">Eigen::PolynomialSolverBase::smallestRealRoot</a></div><div class="ttdeci">const RealScalar &amp; smallestRealRoot(bool &amp;hasArealRoot, const RealScalar &amp;absImaginaryThreshold=NumTraits&lt; Scalar &gt;::dummy_precision()) const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:283</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_ad2438282277bbb62960c3ad1f286052b"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#ad2438282277bbb62960c3ad1f286052b">Eigen::PolynomialSolverBase::absSmallestRealRoot</a></div><div class="ttdeci">const RealScalar &amp; absSmallestRealRoot(bool &amp;hasArealRoot, const RealScalar &amp;absImaginaryThreshold=NumTraits&lt; Scalar &gt;::dummy_precision()) const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:237</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_ade5cd822a659dc18f4e8b674d477bec0"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#ade5cd822a659dc18f4e8b674d477bec0">Eigen::PolynomialSolverBase::absGreatestRealRoot</a></div><div class="ttdeci">const RealScalar &amp; absGreatestRealRoot(bool &amp;hasArealRoot, const RealScalar &amp;absImaginaryThreshold=NumTraits&lt; Scalar &gt;::dummy_precision()) const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:214</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolverBase_html_ae315ff89bf2811db0b9378fdf9bdae11"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#ae315ff89bf2811db0b9378fdf9bdae11">Eigen::PolynomialSolverBase::roots</a></div><div class="ttdeci">const RootsType &amp; roots() const</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:57</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolver_html"><div class="ttname"><a href="classEigen_1_1PolynomialSolver.html">Eigen::PolynomialSolver</a></div><div class="ttdoc">A polynomial solver.</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:334</div></div>
<div class="ttc" id="aclassEigen_1_1PolynomialSolver_html_a93d305d8529be0de76019514eb87b086"><div class="ttname"><a href="classEigen_1_1PolynomialSolver.html#a93d305d8529be0de76019514eb87b086">Eigen::PolynomialSolver::compute</a></div><div class="ttdeci">void compute(const OtherPolynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:350</div></div>
<div class="ttc" id="agroup__Polynomials__Module_html_gadb64ffddaa9e83634e3ab0e3fd3664f5"><div class="ttname"><a href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">Eigen::poly_eval</a></div><div class="ttdeci">T poly_eval(const Polynomials &amp;poly, const T &amp;x)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:48</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a04d60a3c8a266f63c08e03615c1985c9"><div class="ttname"><a href="../namespaceEigen.html#a04d60a3c8a266f63c08e03615c1985c9">Eigen::imag</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_imag_op&lt; typename Derived::Scalar &gt;, const Derived &gt; imag(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a54cc34b64b4935307efc06d56cd531df"><div class="ttname"><a href="../namespaceEigen.html#a54cc34b64b4935307efc06d56cd531df">Eigen::abs2</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs2_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs2(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div></div>
<div class="ttc" id="anamespaceEigen_html_ac74dc920119b1eba45e9218d9f402afc"><div class="ttname"><a href="../namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">Eigen::real</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_real_op&lt; typename Derived::Scalar &gt;, const Derived &gt; real(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="../structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div></div>
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